Fleet Assignment with Time Windows, Spacing Constraints and Time Dependent Profits

Given the sets of flights and aircraft of an airline carrier, the fleet assignment problem consists in assigning the most profitable aircraft type to each flight. An extension to this problem is to allow for some flexibility on flight departure times. These time adjustments increase the number of possible connections and therefore improve the solution quality in terms of profits or in the reduction of the number of aircraft used to cover all flights. However some adjustments should be done with care. For instance, if the departure times of two flights serving the same origin-destination pair of cities become too close, passenger demands may be overestimated. Since passenger demands depend on departure times, flight profits may as well be inaccurate in case of a large flexibility. Therefore it is important to control not only the size of the time windows on flight departures but also the spacing out between flights serving the same O-D pair and the demand estimations.